I haven't seen this yet, but it might be in the FAQ or rules.

If the Admiral draws a Desination card with a mandatory, non-resource, cost that the humans cannot afford -- such losing a Raptor (Remote Planet) or draw and destroy a civilian ship (Misjump) if all of them are already gone -- then can the Admiral choose that card?

If no, what happens if both cards have a mandatory, non-resource cost that the humans cannot pay?

I think, the admiral can choose such a destination.

I have to review destinations, but I am not sure of any and that are requirement worded such as "Destroy a raptor and ...."

For the consequence, like discarding skill cards for water shortage, if you don't got it to lose then nothing happens. You have to comply with a result if you can.

Remote Planet (2): "Lose 1 fuel and destroy 1 raptor."

Misjump (0): "Draw 1 civilian ship and destroy it. Then discard this card and draw a new Destination Card to resolve."

New answer to the question is "Yes".....

You select a card, and what is on the card are the instructions for AFTER you play it. (See base book: jumping the fleet). If you don't have a raptor to destroy, or enough fuel, etc... you do as much as you can and thats it.

The card is the "after effect" of the jump, not the cost.

If wihtin that consquence it has a cost option... i.e. "risk a raptor to..." you would have to have that component to do complete that section.